A very broad answer is that all of these meanings are possible, but some interpretations tend to take precedence over others when there is ambiguity, and in some cases you need to disambiguate. I've added some more details in my answer below.
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Neil CoffeyNov 27 '12 at 16:46

3 Answers
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You can't use every verb in its so-called “pronominal” form, but as you have probably observed given your examples, a large majority of verbs potentially can. Now, which can be used where stems to some extent from the range of possible interpretations of a pronominal verb. Let's remind ourselves of the potential possibilities across the language as a whole:

again, the pronoun can be indirect: ils s'achètent des glaces can mean “they're buying one another ice creams”;

intrinsic: where the verb is pronominal, “just because it is”. For example, in ils se souviennent de…, there's no real sense in which se means eux-mêmes or l'un l'autre; similarly, in il s'agit de…, there's not really any meaning to or anything you could replace the se with (these cases essentially spring up for historic reasons that we won't go into here);

a middle construction: a kind of “non-punctual passive where an agent is implied but not stated”: ce vin se boit chambré (but it sounds odd to say ?“ce vin s'est bu par mes amis” compared to a “genuine” passive where you can introduce an agent and punctual time point: Ce vin a été bu par mes amis);

a “neutral” passive equivalent: expressing a punctual time, but potentially ambiguous as to whether there was an agent, though one can be specified: le verre s'est cassé; la maison s'est remplie de fumée. When there is no agent, this is sometimes called an “ergative” construction.

So, which can be used with which verbs?

Well, in general:

most verbs that can take a complement (direct or indirect) can be used with the reflexive or reciprocal interpretation, but are potentially ambiguous between the two;

if there is genuine ambiguity, then you need to insert a phrase to disambiguate, mutuellement, réciproquement, l'un l'autre, entre eux…

most verbs that could normally be transitive (with a direct complement) with a subject that indicates the “agent” of the action can be turned into a pronominal version with a “middle” interpretation where you are implying a “habitual” interpretation — or put more simply, Le vin se boit chambré works because boire is the type of verb where “some specific thing or person can be doing the drinking”, and you are expressing a generality;

an intrinsic interpretation will generally take precedence, so other interpretations become more difficult if an intrinsic interpretation is available. For example, speakers would usually not use il s'est ri to mean “he laughed to himself”, because there is a conflicting construction se rire de… meaning “to make fun of”, so you need to find another way to say it, e.g. il a ri intérieurement.

a reflexive/reciprocal/passive interpretation tends to take precedence over a middle construction if there is otherwise ambiguity: so la porte s'ouvrait will tend to be interpreted as “the door was opening at that moment”, and not “the door could be opened” or “the door generally used to open”, but you could add a phrase to disambiguate and potentially get either interpretation (cf “La porte s'ouvrait au moment où je suis arrivé.” vs “Généralement, la porte s'ouvrait facilement.”).

for verbs where there is no “agent” (the “ergative” case), as in le verre s'est brisé meaning simply “the glass smashed” rather than “the glass was smashed by…”, things are unfortunately a bit more arbitrary: some verbs allow you to use an intransitive as in English (e.g. La maison brûlait, La roue tournait) whereas others require the pronominal construction (you can't say le verre a brisé: it has to be s'est brisé). I think things are a bit arbitrary in this case, though there is a slight trend in the language towards allowing plain intransitives in “scientific” use where normally one would expect a pronominal ergative. So while you might have expected la substance s'est cristallisée, you will in reality also find la substance a cristallisé with essentially the same interpretation.

Generally, if you want to say “I will do something at/to/on me=myself”, you can use “se faire quelque chose”, as in the examples you give (“I wash myself”, “I told myself”, etc.)

Hence, yes, “je m'aime” is “I love¹ myself”.

Now, an important part of the usage of “se” is pronominal verbs, seemingly called “reflexive” in English. There's much to say on the subject, but basically

the subject(s) performing the action of the [pronominal] verb are the same as the object(s) being acted upon.

To teach yourself how to paint, that'll be “je m'​apprends à peindre” ( m' being the first person reflexive pronoun “me” in front of a vowel). It sounds strange though, because “j'apprends à peindre”, i.e. “I'm learning how to paint” is simpler, like in English.

For them to fight each other, “ils vont se battre entre eux”. If you remove “entre eux”, you can't tell if they'll fight each other or against something else.

Se is a pronoun. It is used as direct and indirect object designating the same person or thing as the subject in verbs at the third person. To designate something else, use le, la, les, the speaker use me, nous and the person(s) to whom one speaks, use te, vous.

Then there is the class of pronominal verbs for which the use of a reflexive pronoun (se at the third person, me, nous at the first, te, vous at the second) changes the meaning and for which the function of the reflexive pronoun is not well defined. Trying to analyze them is doomed for the same kind of partial success as trying to analyze phrasal verbs in English by separating the verb and the preposition.

In il se lave we are clearly in the first situation.

In Paul se dit..., we are perhaps in a case where a verb is becoming pronominal, you better analyze that as Paul dit à lui-même..., but it is acquiring a slightly different meaning (and different from the impersonal use of il se dit).

In il s'appelle Paul, the verb has become pronominal in this use (he is named Paul is a better translation than he calls himself Paul) but you can somewhat get the meaning from a simple analysis.

In il s'ennuie, the meaning is clearly different (he is bored, not he is annoying himself).